An Atom, in the context of games, refers to the smallest possible unit of gameplay which can still be considered as “playing the game”. As this definition is somewhat loose, what does and does not count as a given game’s atom will be subjective.
Here’s a few examples of different games and what I consider to be their atoms, to help illustrate some points later on.
The length and frequence of an atom has a significant impact on gameplay feel.
A game with a short atom would allow for players to quickly pick up or put down the game, as the distance between them and what they view as “fun” is very minimal. You may notice that many party games tend to have short atoms due to this very reason - ease of pickup. However, short atoms would limit the game’s depth as you cannot have too much “game state” persisting between each atom and the next, otherwise you risk making this persistence too important to the feel of play and making the atom larger as a result.
Long atoms come with the obvious downside of being very hard to pick up - you have to commit to sitting down and playing, because if you leave too early you may not even finish a single atom and come out unsatisfied. However, a longer atom allows for more depth and richness as it is assumed the player fully commits to play: notice how TTRPGs and chess both have very long atoms.
The frequency of an atom is also a factor of concern. You may initially think that there’s no period of play without an atom, but consider Poker - if you fold, but the other people are still playing, you are not part of an active atom and need to wait to rejoin. The more infrequent the atoms are, the more downtime there is, and the game is either percieved as calmer, or less serious. Note that “less serious” is not necessarily bad - in a party game, you want to allow players the freedom to get up between atoms to go get a drink or go to the bathroom. More on this analysis on the page for Downtime.